\chapter[Optimisation \\ \textnormal{\emph{Lectured in Easter \oldstylenums{2021} by \textsc{Dr.\ V.\ Jog}}}]{Optimisation}
\emph{\Large Lectured in Easter \oldstylenums{2021} by \textsc{Dr.\ V.\ Jog}}

Many real-world problems involve finding optimal points of functions, for instance making the most valuable products given limited resources, or finding the optimal way to transport goods across a network.
In this course, we study the theory behind optimisation, and produce various algorithms for computing optima in different environments.

An important class of functions is the convex functions.
One can show that if a function is convex, we can use local behaviour to make conclusions about global minima and maxima.
This helps guide our study of optimisation.
Linear functions are convex, and the study of optimising linear functions is called linear programming.
We show that linear programs can be solved computationally using the simplex method, allowing us to easily solve lots of real-world optimisation problems.

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